ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to 

ΔABC is similar to ΔDEF. Length of AB is 18 cm and  length of the corresponding side  DE is 10 cm. What is the ratio  of Perimeter of ΔABC : Perimeter of ΔDEF?

ABCD is a cyclic quadrilateral and AD is a diameter. If ∠DAC=55° then value of ∠ABC is

The length of the common chord of two circles of radii 30 cm and 40 cm whose centers are 50 cm apart is (in cm) 

 If $$ {x=7-4\sqrt{3}}$$ find the value of $$ {\sqrt{x}+{1\over {\sqrt{x}}}}$$.

In ΔABC, AB = AC and ∠B = 40 °, find the value of ∠A.

In a circle, PQ is diameter, RS is chord of length equal to radius of circle. PR and QS when produced intersect at point T. Find the ∠PTQ?